'Total return, when measuring performance, is the actual rate of return of an investment or a pool of investments over a given evaluation period. Total return includes interest, capital gains, dividends and distributions realized over a given period of time. Total return accounts for two categories of return: income including interest paid by fixed-income investments, distributions or dividends and capital appreciation, representing the change in the market price of an asset.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (63%) in the period of the last 5 years, the total return of 47.2% of ProShares Ultra Dow30 is lower, thus worse.
- Compared with SPY (33.5%) in the period of the last 3 years, the total return, or increase in value of 23% is lower, thus worse.

'The compound annual growth rate (CAGR) is a useful measure of growth over multiple time periods. It can be thought of as the growth rate that gets you from the initial investment value to the ending investment value if you assume that the investment has been compounding over the time period.'

Applying this definition to our asset in some examples:- Looking at the annual return (CAGR) of 8% in the last 5 years of ProShares Ultra Dow30, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (10.3%)
- Compared with SPY (10.1%) in the period of the last 3 years, the compounded annual growth rate (CAGR) of 7.1% is lower, thus worse.

'Volatility is a statistical measure of the dispersion of returns for a given security or market index. Volatility can either be measured by using the standard deviation or variance between returns from that same security or market index. Commonly, the higher the volatility, the riskier the security. In the securities markets, volatility is often associated with big swings in either direction. For example, when the stock market rises and falls more than one percent over a sustained period of time, it is called a 'volatile' market.'

Applying this definition to our asset in some examples:- The volatility over 5 years of ProShares Ultra Dow30 is 42.9%, which is larger, thus worse compared to the benchmark SPY (21.6%) in the same period.
- Looking at volatility in of 49.3% in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (25.1%).

'Downside risk is the financial risk associated with losses. That is, it is the risk of the actual return being below the expected return, or the uncertainty about the magnitude of that difference. Risk measures typically quantify the downside risk, whereas the standard deviation (an example of a deviation risk measure) measures both the upside and downside risk. Specifically, downside risk in our definition is the semi-deviation, that is the standard deviation of all negative returns.'

Using this definition on our asset we see for example:- Looking at the downside deviation of 31.1% in the last 5 years of ProShares Ultra Dow30, we see it is relatively larger, thus worse in comparison to the benchmark SPY (15.6%)
- Looking at downside deviation in of 35.5% in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (18.1%).

'The Sharpe ratio was developed by Nobel laureate William F. Sharpe, and is used to help investors understand the return of an investment compared to its risk. The ratio is the average return earned in excess of the risk-free rate per unit of volatility or total risk. Subtracting the risk-free rate from the mean return allows an investor to better isolate the profits associated with risk-taking activities. One intuition of this calculation is that a portfolio engaging in 'zero risk' investments, such as the purchase of U.S. Treasury bills (for which the expected return is the risk-free rate), has a Sharpe ratio of exactly zero. Generally, the greater the value of the Sharpe ratio, the more attractive the risk-adjusted return.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (0.36) in the period of the last 5 years, the risk / return profile (Sharpe) of 0.13 of ProShares Ultra Dow30 is lower, thus worse.
- Compared with SPY (0.3) in the period of the last 3 years, the ratio of return and volatility (Sharpe) of 0.09 is lower, thus worse.

'The Sortino ratio improves upon the Sharpe ratio by isolating downside volatility from total volatility by dividing excess return by the downside deviation. The Sortino ratio is a variation of the Sharpe ratio that differentiates harmful volatility from total overall volatility by using the asset's standard deviation of negative asset returns, called downside deviation. The Sortino ratio takes the asset's return and subtracts the risk-free rate, and then divides that amount by the asset's downside deviation. The ratio was named after Frank A. Sortino.'

Which means for our asset as example:- Compared with the benchmark SPY (0.5) in the period of the last 5 years, the downside risk / excess return profile of 0.18 of ProShares Ultra Dow30 is lower, thus worse.
- During the last 3 years, the downside risk / excess return profile is 0.13, which is lower, thus worse than the value of 0.42 from the benchmark.

'Ulcer Index is a method for measuring investment risk that addresses the real concerns of investors, unlike the widely used standard deviation of return. UI is a measure of the depth and duration of drawdowns in prices from earlier highs. Using Ulcer Index instead of standard deviation can lead to very different conclusions about investment risk and risk-adjusted return, especially when evaluating strategies that seek to avoid major declines in portfolio value (market timing, dynamic asset allocation, hedge funds, etc.). The Ulcer Index was originally developed in 1987. Since then, it has been widely recognized and adopted by the investment community. According to Nelson Freeburg, editor of Formula Research, Ulcer Index is “perhaps the most fully realized statistical portrait of risk there is.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (8.88 ) in the period of the last 5 years, the Downside risk index of 17 of ProShares Ultra Dow30 is higher, thus worse.
- Looking at Ulcer Ratio in of 21 in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (11 ).

'A maximum drawdown is the maximum loss from a peak to a trough of a portfolio, before a new peak is attained. Maximum Drawdown is an indicator of downside risk over a specified time period. It can be used both as a stand-alone measure or as an input into other metrics such as 'Return over Maximum Drawdown' and the Calmar Ratio. Maximum Drawdown is expressed in percentage terms.'

Applying this definition to our asset in some examples:- The maximum DrawDown over 5 years of ProShares Ultra Dow30 is -63.1 days, which is smaller, thus worse compared to the benchmark SPY (-33.7 days) in the same period.
- Looking at maximum reduction from previous high in of -63.1 days in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (-33.7 days).

'The Drawdown Duration is the length of any peak to peak period, or the time between new equity highs. The Max Drawdown Duration is the worst (the maximum/longest) amount of time an investment has seen between peaks (equity highs) in days.'

Which means for our asset as example:- Compared with the benchmark SPY (273 days) in the period of the last 5 years, the maximum days under water of 272 days of ProShares Ultra Dow30 is lower, thus better.
- Looking at maximum days below previous high in of 272 days in the period of the last 3 years, we see it is relatively lower, thus better in comparison to SPY (273 days).

'The Average Drawdown Duration is an extension of the Maximum Drawdown. However, this metric does not explain the drawdown in dollars or percentages, rather in days, weeks, or months. The Avg Drawdown Duration is the average amount of time an investment has seen between peaks (equity highs), or in other terms the average of time under water of all drawdowns. So in contrast to the Maximum duration it does not measure only one drawdown event but calculates the average of all.'

Which means for our asset as example:- Compared with the benchmark SPY (57 days) in the period of the last 5 years, the average time in days below previous high water mark of 85 days of ProShares Ultra Dow30 is greater, thus worse.
- Looking at average time in days below previous high water mark in of 100 days in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (73 days).

Historical returns have been extended using synthetic data.
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- Note that yearly returns do not equal the sum of monthly returns due to compounding.
- Performance results of ProShares Ultra Dow30 are hypothetical, do not account for slippage, fees or taxes, and are based on backtesting, which has many inherent limitations, some of which are described in our Terms of Use.